Statistics show that in America, couples who live together before getting married tend to break up, EXCEPT when they are engaged when they move in.

But at this point you're in a very tricky situation: If it's a tit for tat, he can easily agree to marry you so you'll move in, and then never follow through.

What about just telling him, "No thank you, I'm not ready", and leave it at that for now, and don't mention "if we were engaged". I realize it's difficult to face the idea of living on your own with a newborn, when you have the option of having more hands around (I was there once too, it's EXTREMELY difficult). Say, give him the month of February to see what happens if you say no thanks? You could still decide to move in with him in March?